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Homework Help: Help finding eigenvectors to simple 2x2 matrix

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Find a fundamental set of real solutions of the system.
    x'=[-0.5 1 ]x
    [-1 -0.5]

    3. The attempt at a solution
    I calculated the eigenvalues to be r1 = -0.5+i and r2 = -0.5-i
    Then, attempting to calculate the eigenvectors,
    I plugged the numbers into the system
    [-0.5+0.5-i 1][v1] = [0]
    [-1 -0.5+0.5-i ][v2] [0]
    which simplifies to be
    [-i 1] [v1] = [0]
    [-1 -i ][v2] [0]
    afer matrix multiplication, I get two formulas
    -1(v1)i+(v2)=0
    -1(v1)-(v2)i=0
    However, I am at a loss for the next step. Usually when I am finding the eigenvector those two equations will have the same ratio. Please advise.
     
  2. jcsd
  3. Mar 12, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Your two formulas do have the same ratio:wink:...Just multiply the second equation by [itex]i[/itex].
     
  4. Mar 12, 2010 #3
    thanks guy! I can't believe i didn't see that!
     
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